# Homework Help: Real analysis question

1. Sep 28, 2011

### Maybe_Memorie

1. The problem statement, all variables and given/known data

Let f:Rnxn-->Rnxn be defined by f(A) = A2. Prove that f is differentiable. Find the derivative of f.

2. Relevant equations

f(a + h) = f(a) + f'(a)h + $\phi$(h)

3. The attempt at a solution

f(A + H) = (A + H)2 = A2 + AH + HA + H2

f(A) is given by A2. So the sum of the derivative operator and the remainder term is AH + HA + H2. The problem is that I don't know how to determine which terms are part of the derivative.

2. Sep 28, 2011

### Office_Shredder

Staff Emeritus
The derivative is the linear part of AH+HA+H2 in H. So the question is which part is linear and which part is not?